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Mirrors > Home > MPE Home > Th. List > brsdom2 | Structured version Visualization version Unicode version |
Description: Alternate definition of strict dominance. Definition 3 of [Suppes] p. 97. (Contributed by NM, 27-Jul-2004.) |
Ref | Expression |
---|---|
brsdom2.1 | |
brsdom2.2 |
Ref | Expression |
---|---|
brsdom2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfsdom2 8083 | . . 3 | |
2 | 1 | eleq2i 2693 | . 2 |
3 | df-br 4654 | . 2 | |
4 | df-br 4654 | . . . 4 | |
5 | df-br 4654 | . . . . . 6 | |
6 | brsdom2.1 | . . . . . . 7 | |
7 | brsdom2.2 | . . . . . . 7 | |
8 | 6, 7 | opelcnv 5304 | . . . . . 6 |
9 | 5, 8 | bitr4i 267 | . . . . 5 |
10 | 9 | notbii 310 | . . . 4 |
11 | 4, 10 | anbi12i 733 | . . 3 |
12 | eldif 3584 | . . 3 | |
13 | 11, 12 | bitr4i 267 | . 2 |
14 | 2, 3, 13 | 3bitr4i 292 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wb 196 wa 384 wcel 1990 cvv 3200 cdif 3571 cop 4183 class class class wbr 4653 ccnv 5113 cdom 7953 csdm 7954 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 ax-un 6949 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-er 7742 df-en 7956 df-dom 7957 df-sdom 7958 |
This theorem is referenced by: (None) |
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